Write equations of lines when given two points and write equations of lines from a graph

Emma Wheatley, Emmi Shearman, Katherine King, Makenzie Carter

Necessary Formulas:

1. Y=mx+b
2. (y-y1)=m(x-x1)
3. y2-y1
x2-x1
4. rise
run

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by Emma Wheatley

Emmi Shearman

The line through two distinct points (x1, y1) and (x2, y2) is given by

(1)	y = y1 + [(y2 - y1) / (x2 - x1)]·(x - x1),

where x1 and x2 are assumed to be different. In case they are equal, the equation is simplified to

x = x1

and does not require a second point.
Equation (1) can also be written as

y - y1 = [(y2 - y1) / (x2 - x1)]·(x - x1),

or even as

(x2 - x1)·(y - y1) = (y2 - y1)·(x - x1),

where one does not have to worry whether x1 = x2 or not. However, the simplest for me to remember is this

(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)

which is not as universal is the one before.


Practice Problems and Helpful websites.
Katherine King

Things to know

• equation of line: y=mx+b
• m is the slope
• b is the y-intercept
• The slope of a line - a measure of how fast the line "goes up" or "goes down".
  • A large slope means the line goes up or down really fast (a very steep line).
  • Small slopes means the line isn't very steep.
  • A slope of zero means the line has no steepness at all; it is perfectly horizontal.
• Equation for the slope

Write the equation of the line when given the points (3,2) (7,4)
Answer : y = 1/2x+1/2

Websites
Help website 1
Help Website 2

Makenzie Carter
Formulas:
Slope: for a given two points, (x1, y1) and (x2, y2); m = y2 - y1
x2 - x1
Slope- Intercept Equation: y = mx + b

Point- Slope Equation: for a given point (x1, y1) and slope, m, (y - y1) = m(x - x1)

Example:
Find the slope of the line

Work:
m = y2 - y1
x2 - x1

m = 3 - (-3)
-3 - 1

m = 6
-4

m = - 3
2